How to hide the object emitting particles in a render in Blender 2.80?
There are two settings Show emitter:


in the Render section works only for the final render
in the Viewport Display section for the current view port 


However when you un-check the Show emitter in the Viewport Display section both emitter and particles may disappear. You need to re-select Dispaly As as Rendered and then only the particles will show.

To hide the original object or collection used for particle instances just hide them in Scene collection window.